If we look at BOLT 02 funding_locked
we can see that we have to differentiate between two cases.
the funding party "MUST wait until the funding transaction has reached minimum_depth
before sending this message." This means it is the funding parties responsibility to get the funding tx confirmed. It can basically do so by doing CPFP on the change output or RBF (if that is supported)
"A non-funding node (fundee) SHOULD forget the channel if it does not see the correct funding transaction after a timeout of 2016 blocks." Which means that as soon as opening is negotiated and the fundee doesn't see the funding tx confirmed it will forget the channel.
also the BOLT says:
From the point of waiting for funding_locked
onward, either node MAY send an error
and fail the channel if it does not receive a required response from the other node after a reasonable timeout.
So basically the channel will be closed before being opened if the funding transaction does not confirm within a reasonable time. (For some suitable definition of reasonable (meaning it is not exactly specified))